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Thad Szabo
Attended University of Pennsylvania
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Thad Szabo

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Here's what Jupiter does in about an hour. I had clouds move in part way through this, so I have more sporadic frames stretching for another 90 minutes or so. This is from 0400 to 0500 UT on 2015-03-14. All frames shot with a Point Grey Flea 3 and Celestron Edge HD 9.25" scope at f/10. Stacking in Autostakkert and final processing in GIMP. 

That brightest dot heading away from Jupiter? That's Ganymede - the largest moon in the solar system. It's the only one that has its own magnetic field, and as such it also has aurorae. The Hubble Space Telescope observed these aurorae recently, and their small fluctuations make a good case for an enormous ocean of salty water under Ganymede's surface.
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Nice animation +Thad Szabo​ nice to see how much movement happens in the course of a single hour. 
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Heads up to all planetary photographers (like +Michael A. Phillips, +Mitchell Duke, +Stuart Forman, and others in North America)!

One of the projects I had my lab students work on this past semester when we got clouded out was finding as many of the occultations, eclipses, and multiple shadow transits of Jupiter's Galilean moons. Starting at 2015-01-24 about 04:00 UT, get setup for a gorgeous 3-D display. Both the shadow of Io and Callisto can be seen on the Jovian disk starting around 04:30 UT. Europa's shadow joins the bunch for a triple shadow transit about 06:25 UT. The triple shadow transit lasts a bit under 30 minutes, then we're back down to two shadows for the next 70 minutes.  This one is well placed for observers in the U.S. and Mexico.
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+Mitchell Duke like 2 weeks till opposition? 
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I just borrowed one of our department's solar filters and confirmed that AR 2192 is plainly visible to the naked eye. Get some proper eye protection and see for yourself.
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Did any other solar imagers catch this giant feature off the sun's limb today? The photo is from a Coronado 60mm H-alpha SolarMax scope (no tracking, no guidance) and 250 of 800 frames from a Point Grey Flea3 camera, both of which belong to the Physics and Astronomy Department at Cerritos College. This is my first time trying to image the sun with this scope. At 120 frames per second, there wasn't much drift, and AutoStakkert handled the composition pretty cleanly. Final processing in GIMP. Image shot at 2014-10-15 2340 UT.
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Raining at my end. Would be a nice target to image though. 
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Superclusters!

The original Nature paper by Tully, Courtois, Hoffman, and Pomarède (Nature 513, 71-73 (2014)) is behind a firewall, and I can't find it on arxiv.org. However, they created a wonderful movie with 3-D representations of their work on peculiar velocities that leads to an understanding of the idea of the local supercluster, #Laniakea . The movie is linked to this post. It's a little over 17 minutes long, but it's worth watching if you want a better understanding of the full scope of what they have discovered.

My research is on galaxy clusters -- the largest gravitationally bound structures in the Universe. What has always bothered me about the idea of a "supercluster" is that, if you keep the Hubble flow present (which makes sense, since it exists), the various clusters that make up a supercluster will not join together. We see this in surveys of galaxy clusters. There is a maximum size. We do not find galaxy clusters with more than about 3x10^15 solar masses. If clusters could continue to merge under gravity, some of them would have done so by now and produced clusters bigger than this size. This is also evidence for dark energy. The density of a region can overcome the Hubble expansion locally and cause matter to fall inwards. The largest regions over which we see this behavior are galaxy clusters. Without dark energy, the Hubble expansion would decrease at a rate that would allow mergers of clusters into larger gravitationally bound structures. The fact that the rate of decrease does not allow this to happen indicates that the gravity produced by the galaxies is insufficient to describe the behavior of the Universe. The distribution of sizes of galaxy clusters show that there must be more than atoms and dark matter. We don't know what "dark energy" is, but we can't explain the structure of the Universe without it.

But what if you subtract out the Hubble expansion? We have redshift data on enough galaxies to be able to do this. Also, if we make measurements independent of redshift, such as through variable stars (Cepheids or Type Ia supernovae) or the Tully-Fisher relation, we can get a sense of distance independent of redshift measurements. Subtract redshift velocity measurements from the Hubble expansion adjusted for independent distance measurements and you get "peculiar velocities." These are the velocities that galaxies have relative to the cosmic microwave background (CMB) when the expansion of the Universe is removed.

Is your mind blown yet? Just wait. What the group that made this movie did was plot these peculiar velocities for thousands and thousands of galaxies. If you watch the movie, distances are measured in kilometers per second. Hopefully, that triggers a warning for most of you -- "Km/s is velocity, not distance!" However, the measured speed of expansion of the Universe relative to our vantage point in the Milky Way -- and relative to any vantage point -- depends on the distance from that point. The best estimates we have put this relationship at about 70 km/s/Mpc*. Thus, for every megaparsec you move through space from an observer, the expansion of the Universe carries your positions away from each other 70 km/s faster. The authors of the paper use this relationship to indicate the distance in their movie. It also let's you know the value they are subtracting to get the peculiar velocities.

Tully, et al, appear to share my view that, until this work, the idea of a supercluster was ill-defined. Measuring the flow of galaxies from mapping their peculiar velocities gives a much clearer definition. Look for boundaries in the patterns of divergent flows, and you can determine the boundaries of the superclusters.

Like our own supercluster, Laniakea.

*There will probably be some dissent over my choice of 70 km/s/Mpc for the Hubble constant. WMAP and Type Ia supporters will want a value closer to 73 km/s/Mpc. Planck supporters will want a value closer to 68 km/s/Mpc. This matter is not settled, so I'm going to round off to 1 significant figure and say 70 km/s/Mpc. This is too complicated a matter to expand upon in this footnote. 
This movie can also be viewed and downloaded in HD, SD, and Mobile versions at http://vimeo.com/pomarede/cosmography. The FullHD version is available for viewing and download at http://vimeo.com/pomarede/cosmographyfhd. The version commented in french is available for viewing and download at ...
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My students who are learning their way around Linux need to see this...
 
There's a lot of folks that will understand this, and then there's a lot of folks that won't.

#HammerTime   #chmod   #mkdir   #YouCantTouchThis  
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I...damn I got it right away. Nice touch.
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This sounds like Bear McCreary met up with an early 90s industrial band. That is a good thing, and hard to believe this is all possible with one instrument.

At some point, I have to understand that I'm not going to be able to play all the instruments, or speak all the languages, or do all the math and science, and just enjoy performances like this.
On a list of things I most anticipated sitting down to cover on Colossal today, the hurdy gurdy probably wasn't in the top thousand topics, but then I stumbled onto this video and had to share it. The piece is called Omen, written and performed by Guilhem Desq, who uses an electrified version
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wow super!
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It's always fun to learn how to generate new sequences and learn their properties! Also, as my wife pointed out, this would make a cool tiling to do on a wall.
 
The plastic number

The sequence of side lengths of equilateral triangles in this picture form the Padovan sequence (1,1,1,2,2,3,4,5,7,9...). Just as the Fibonacci sequence is governed by the properties of the golden ratio, the Padovan sequence is governed by the properties of the so-called plastic number.

The Padovan sequence P(n) is sequence is defined by setting P(1)=P(2)=P(3)=1, and then requiring P(n) = P(n–2) + P(n–3) for n > 3. The generating function for the sequence is given by G(x)=(1+x)/(1–x^2–x^3), which means that if this ratio of polynomials is expanded as a power series in x, the coefficient in G(x) of x^n (i.e., x to the nth power) is equal to P(n). 

The denominator in the formula for the generating function, 1–x^2–x^3, can be regarded as an algebraic encoding of the recurrence relation P(n)–P(n–2)–P(n–3)=0. An easy calculation involving polynomials shows that the product (1–x^2–x^3)(1–x+x^2) is given by 1–x–x^5. This means that the generating function G(x) can be rewritten so that the denominator polynomial is given by 1–x–x^5, which in turn means that, if n is large enough, the sequence will satisfy the recurrence relation P(n) = P(n–1) + P(n–5). 

The picture is an illustration of this last relation. Notice that the big triangle with side 16 is bounded on one side by the preceding triangle in the sequence (of side 12) and the triangle five places earlier in the sequence (of side 4). This corresponds to the fact that P(n) = P(n–1) + P(n–5) for n=12 and P(n)=16.

It turns out that the polynomial 1–x^2–x^3 has exactly one real root, and the plastic number is the reciprocal of this root. Another way to say this is that the plastic number is the unique real solution of the equation x^3=x+1. It is not hard to show using abstract algebra that this solution is an irrational number; the same is true for the golden ratio, which is the larger real solution of the equation x^2=x+1. The decimal expansion of the plastic number is therefore non-recurring; the first few digits are 1.324717957..., and over 10,000,000,000 digits have been computed. 

The plastic number is mathematically significant because it is the smallest Pisot number. A Pisot number is a real root of a monic integer polynomial whose other roots are complex numbers of absolute value less than 1. The word monic means that the highest power of x occurring has a coefficient of 1. The connection with the Padovan sequence is that the ratio P(n+1)/P(n), as n becomes large, tends to the plastic number. (In the case of the Fibonacci numbers, the corresponding ratio approaches the golden ratio.)

The Padovan sequence was described by Richard Padovan in a 1994 essay about the Dutch architect Hans van der Laan. Padovan attributed the discovery of the sequence to van der Laan, so van der Laan sequence would have been a more historically accurate name. The reason for the name plastic is too weak to explain convincingly, but it is intended to convey the sense of something that can be given a three-dimensional shape.

The Padovan sequence has several fairly natural interpretations. One of these is that P(n) is the number of ways of writing n+1 as an ordered sum in which each term is either 2 or 3. For example, P(7) is 4, and this corresponds to the four ways in which 7+1=8 can be written as an ordered sum of 2s and 3s: 8 = 2+2+2+2 = 3+3+2 = 3+2+3 = 3+3+2.

Relevant links

Wikipedia on the plastic number: http://en.wikipedia.org/wiki/Plastic_number

Wikipedia on Pisot numbers, also known as Pisot–Vijayaraghavan numbers or PV numbers: http://en.wikipedia.org/wiki/Pisot–Vijayaraghavan_number

Wikipedia on the Padovan sequence, where this picture comes from: http://en.wikipedia.org/wiki/Padovan_sequence

The Padovan sequence at the On-Line Encyclopedia of Integer Sequences: http://oeis.org/A000931 
(Note that the encyclopedia version contains some additional terms at the beginning relative to the definition of the sequence used here.)

Irrelevant link
I now have the 1969 song Plastic Man by the Kinks (http://goo.gl/6dcpbO) stuck in my head. The BBC refused to play the song when it came out because it contains the word “bum”.

(Picture found via Shecky R and Cliff Pickover on Twitter.)

#mathematics #scienceeveryday  
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Ascribing meaning to synchronicity in life events is mistaking the noise for the signal. Be patient.
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Monumental !!
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My brother is vlogging to promote conversation about mental health issues. A key component missing from most discussions is addressing self-hatred. What do you do to cope with it?
 
a vlog about the one thing we're missing when we talk about suicide.
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Wow, keep up the vlog. There are parts in this one that I can certainly relate to.

For me, it wasn't so much the self hatred, but the sense of losing my usefulness and direction. Couldn't do the career that I had been doing for nearly 30 years any more, and when I went to get retrained into something else, the opportunities for employment simply were not there.
Felt that that I had lost nearly everything that I had ever worked for.  

Luckily, I didn't get into drugs or alcohol, and I had friends who stopped me from going too far down the path of destruction (I was about 2 weeks from killing myself). 

These days, still not employed, but I got help and am transitioning to a better place. I liken it to being a recovering addict or alcoholic - The suicide option is always there,  lurking in the background. As long as I know it's still there, I'm OK. It's when I thinks it's gone or think I don't need to be concerned about it, that I need to be on alert.
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Many of us posted contemplative pieces on Robin Williams' suicide. My brother, +Ross Szabo, wrote an article that is a call to action on mental health.
The stigma of mental illness is often believed to be that we don't talk about mental illness. The harsh reality is that people don't talk about their emotions period and a large percentage of people feel that mental illness isn't treatable. We need t...
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I posted a shot to flickr, similar to the one here, from when I visited my brother in Botswana in July 2011 where I cropped the bottom part because of not wanting to deal with the noise in that part of the photo. This portrait oriented shot wouldn't stand for that if I wanted to include the Large Magellanic Cloud. I hit it repeatedly with the Dynamic Background Extraction tool in PixInsight along with multiple noise reductions and color calibrations. The end result may be a bit blue for some astrophotographer's tastes, but I feel like I was able to pull out the LMC, even though it was less than 10 degrees off the horizon.

It also occurred to me as I was working on this - what if these are the only shots I ever get that include the LMC? I have vague plans to return to the Southern Hemisphere. If it doesn't happen, it's all the more imperative that I learn how to make the most of the shots I did get. 

I've been making observations of the sky for most of my life and have had the good fortune to travel to some very dark locations. Usually, there's enough stray light to find my way or my equipment because of some nearby light source. Here, on the northeast shore of the Sua Pan, was the first time I couldn't see 10 feet in front of me at all. This is a stack of 9 untracked, unguided 13 second exposures at ISO 3200 with a Canon T1i at f/3.5 with an 18-55mm lens at 18.0 mm focal length. Thank you to +Ross Szabo for letting me borrow his camera while I was there.

I need to be under skies this dark again. I hope that happens soon.
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Beautiful work. As a fan of space exploration, science fiction and science fact, I love night sky images like this. I even named our film production studio Starfield Studios for this reason. Keep up the great work. :)
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Faculty member in Department of Physics and Astronomy
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Amateur professional/professional amateur astronomer
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Faster than a speeding Kuiper Belt Object. More powerful than a nebulous zephyr. Able to shoot deep sky objects in a single photon.
Education
  • University of Pennsylvania
    Physics, 1988 - 1993
  • Florida State University
    Physics, 1993 - 1997
  • University of Southern California
    Physics, 2004 - 2010
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